Adding Integers
−4+7
3
How to solve:
The signs are different, so subtract the absolute values:
7−4=3
Keep the sign of the number with the greater absolute value.
8−3
5
Subtracting 3 means move 3 units left from 8.
(−4)(3)
−12
Negative × positive = negative.
Using integer counters, model:
+3+(−3)
What is the answer?
Pair each positive counter with a negative counter:
🟦🟥 🟦🟥 🟦🟥
Each pair is a zero pair.
0
Key idea:
A positive and negative of the same value cancel to make zero.
The temperature is −4°F in the morning. By afternoon, it increases 12°F. What is the afternoon temperature?
−4+12=8
8∘F
−8+(−5)
−13
How to solve:
Both integers are negative, so add the absolute values:
8+5=13
Keep the negative sign:
−13
Rule: Same signs → ADD and KEEP the sign.
5−(−4)
9
Integer rule:
Subtracting a negative becomes adding a positive:
5−(−4)=5+4=9
Memory phrase:
Keep, Change, Change.
(−24)÷(−6)
4
Negative ÷ negative = positive.
Use a number line to model:
−2+5
Start at −2.
Adding +5 means move 5 units right.
Land on +3.
3
A diver is at −25 feet. She rises 9 feet. What is her new position?
−25+9=−16
−16 feet
Use a number line to solve:
6+(−9)
−3
How to model:
Start at 6.
Adding −9 means move 9 units left.
You land on −3.
6→−3
−7−6
−13
How to solve:
Change subtraction to addition:
−7−6=−7+(−6)
Same signs → add:
7+6=13
Keep the negative sign.
−13
Complete the rule:
Positive × Negative = ______
Negative
Use integer counters to model:
−5−(−2)
Start with five negative counters:
🔴 🔴 🔴 🔴 🔴
We need to take away 2 negative counters.
Remove two:
🔴 🔴 🔴
Three negative counters remain.
−3
A bank account has a balance of −$35. A deposit of $50 is made. What is the new balance?
−35+50=15
$15
−15+9
−6
How to solve:
Different signs → subtract:
15−9=6
The larger absolute value is 15, which is negative.
−6
−12−(−8)
−4
Change subtraction to addition:
−12+8
Different signs → subtract:
12−8=4
The larger absolute value is 12, so the answer is negative.
−4
−3(−5)+(−8)
7
First multiply:
−3(−5)=15
Then add:
15+(−8)=7
Remember: Follow the order of operations.
A student models
4−7
on a number line.
What direction should the student move?
Start at 4.
Subtracting 7 means move 7 units left.
4→3→2→1→0→−1→−2→−3
−3
A football team loses 8 yards on one play and gains 15 yards on the next play. What is the net change?
−8+15=7
7 yards
The team has a net gain of 7 yards.
A submarine is at −18 meters. It rises 11 meters. What is its new position?
−18+11=−7
The submarine is now:
−7 meters
Model: Start at −18 and move 11 units toward zero.
A temperature is −6°F. It decreases another 9°F. What is the new temperature?
−6−9
Change subtraction to addition:
−6+(−9)
6+9=15
Keep the negative sign:
−15∘F
(−36)÷(−4)−7
2
First Divide
(−36)÷(−4)=9
Then subtract:
9−7=2
A student says:
"When I subtract a negative, I always move left."
Is the student correct? Explain.
No.
For example:
5−(−3)=5+3=8
On a number line, subtracting a negative means moving right.
Sentence stem:
"The student is incorrect because subtracting a negative is equivalent to ______."
Answer: adding a positive.
A mountain climber is at −120 feet relative to a reference point. She climbs 45 feet, descends 30 feet, and then climbs another 25 feet.
What is her final position?
−120+45−30+25
Work from left to right:
−120+45=−75
−75−30=−105
−105+25=−80
−80 feet